in this talk, we will discuss the dynamics on teichmüller space and moduli space of square-tiled surfaces. for square-tiled surfaces, one can explicitly write down the $sl(2,\mathbb{r})$-orbit on the moduli space. to study the dynamics of teichmüller flow of the $sl(2,\mathbb{r})$-action, we study its derivative, namely the kontsevich--zorich cocycle (kz cocycle). in this talk, we will define what a kz cocycle is, and by following explicit examples, we will show how one can compute the kz monodromy. this is part of an ongoing work with anthony sanchez.